Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

A building has 10 floors above the basement. If 12 people get into an elevator at the basement, and each choses a floor at random to get out, independently of the others, at how many floors do you expect the elevator to make a stop to let out one or more of these 12 people??

share|cite|improve this question
up vote 3 down vote accepted

HINT: For $k=1,\dots,10$ let $X_k$ be a random variable that takes the value $1$ if at least one person gets off on floor $k$ and $0$ otherwise. The probability that no one gets off on floor $k$ is $\left(\frac9{10}\right)^{12}$, so $$\Bbb E(X_k)=1-\left(\frac9{10}\right)^{12}\;.$$ You want $\Bbb E(X_1+X_2+\ldots+X_{10})$, and expectation is linear, so ... ?

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.